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Counting the number of minimum cuts in undirected multigraphs

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3 Author(s)
H. Nagamochi ; Kyoto Univ., Japan ; Z. Sun ; T. Ibaraki

The problem of counting the number of cuts with the minimum cardinality in an undirected multigraph arises in various applications, such as testing the super-λ-ness of a graph, as described by F.T. Boesch (1986), and calculating upper and lower bounds on the probabilistic connectedness of a stochastic graph G in which edges are subject to failure. It is shown that the number |C( G)| of cuts with the minimum cardinality λ(G) in a multiple graph G=(V,E) can be computed in O(|E|+λ(G)|V|2 +λ(G)|C(G)||V|) time

Published in:

IEEE Transactions on Reliability  (Volume:40 ,  Issue: 5 )